Definition 11.13.8 (Topology of Precompact Convergence).label Let $E, F$ be TVSs over $K \in \RC$, $\mathfrak{K}\subset 2^{E}$ be the collection of precompact subsets of $E$, then the $\mathfrak{K}$-uniform topology on $L(E; F)$ is the topology of precompact convergence.

The space $L_{c}(E; F)$ denotes $L(E; F)$ equipped with the topology of precompact convergence.